Abstract
This paper deals with estimating the lifetime performance index. The maximum likelihood (ML) and Bayesian estimators for lifetime performance index CLX where LX is the lower specification limit are derived based on progressive type-II censored (Prog-Type-II-C) sample from two-parameter power hazard function distribution (PHFD). Knowing the lower specification limit, the MLE of CLX is applied to construct a new hypothesis testing procedure. Bayesian estimator of CLX is also utilized to develop a credible interval. Also, the relationship between the CLX and the conforming rate of products is investigated. Moreover, the Bayesian test to evaluate the lifetime performance of units is proposed. A simulation study and illustrative example based on a real dataset are discussed to evaluate the performance of the two tests.
Highlights
Process capability analysis plays an important role in the quality control field to measure the performance of process in the industry. e lifetime performance index ( process capability index or (PCI)) has been proposed by Montgomery [1] and Kane [2]. e index is used to assess the lifetime performance of electronic units
In the Bayesian approach, for given specified significance level δ, a 100(1 − δ)% one-sided credible interval (CRI) for CLX is derived as pivotal quantity follows
Step 4. e decision rule of the statistical test is provided as follows: if the performance index value c ∉ [LB BS, ∞), it is concluded that the lifetime performance index of the product meets the required level e maximum likelihood (ML) approach uses 100(1 − δ)% one-sided confidence interval (CI) [LB ML, ∞) for CLX instead of 100(1 − δ)% one-sided CRI
Summary
Process capability analysis plays an important role in the quality control field to measure the performance of process in the industry. e lifetime performance index ( process capability index or (PCI)) has been proposed by Montgomery [1] and Kane [2]. e index is used to assess the lifetime performance of electronic units. All process capability indices (PCIs) have been discussed using the assumption that the lifetime of products (units) follows a normal distribution. A lot of papers were studied on the statistical inference for CLX based on various types of censored and progressive censored data for different models of which [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] dealt with progressive censoring from various points of view considering several lifetime distributions and its applications. Soliman et al [18, 19] discussed assessing the life time performance index for exponentiated Frechet distribution using Prog-Type-II-C and progressive first failure censoring scheme.
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